There's a trick to using the MacBook/Pro with the Lid Closed.
(1) With the machine off, hook up all your connectors to your MacBook/MacBook Pro(power, USB/keyboard/mouse, mini-Display Port).
(2) Slide the machine forward so you can crack open the display enough to reach the Power button on the MB/MBP.
(3) Push the Power button and IMMEDIATELY close the lid.
(4) Slide the MB/MBP into place.
If you've done this right, you'll get the grey boot screen you'd see if you were booting up the MB/MBP on its native display. This procedure will also work for both the MB/MBP whether the power connector for the notebook is hooked to it or not. You can use this procedure to boot and run the MB/MBP on its battery while using the LED and an external keyboard and mouse with it, helping to extend the notebook's battery life.
The trick to this is to push the power button enough to ensure the boot is occurring and then to get the lid closed as early in the boot sequence as you can. It might take you a few trials to get it right, but once you do, I think you'll find that using the MB/MBP with your new LED display will be the great, hassle-free experience you were looking for.